AllPairsPfade
AllPairsPfade is a term used in graph theory to denote a class of algorithms and data structures designed to compute, for every pair of vertices in a weighted graph, the shortest path between them and often the exact path itself. The typical problem setup involves a directed or undirected graph G = (V, E) with a weight function w on the edges, where the goal is to determine, for all pairs (u, v), both the distance from u to v and a concrete path that realizes that distance.
In its most common form, AllPairsPfade produces a distance matrix D where D[u][v] equals the length of
Path reconstruction is a key feature of AllPairsPfade, often implemented via a next-hop or predecessor matrix
Applications span network routing, transportation planning, and analysis of global connectivity, where knowledge of all-pairs routes